Originally Posted by arnyk
As usual Amir, you're changing the subject in order to avoid admitting your error.
There was no error. I explained what happens when you capture something. You added the bit on how it plays and then proceeded to call it incorrect.
The steps are not removed by dither, they are removed by low pass filtering in the reconstruction filter.
They are not removed by low pass filter. I demonstrated that with pictures. Since you don't like that, please show how they are removed in the author's real measurements:
If the steps are removed, why are those distortion spikes still there? Isn't it because the reconstruction filter for 44.1 Khz sampling is at 22.05 Khz and therefore it cannot possibly remove distortions at 300, 500, 700 Hz and such as shown in the above measurement?
Amir, you've compounded your rookie errors by citing a highly flawed source of misinformation about dither. It purported to show the effects of 16 bit sampling, when in fact it showed the effects of 8 bit sampling.
Not at all. You didn't appreciate the points I and Rock_bottom made. You proceeded to add your own information to his measurements such as it being a -6 db down from full scale digital whereas he clearly said it was a "low level signal" A -6dbfs is essentially a full scale signal. There is nothing about that is "low level."
If we follow the test conditions as he describes, then we see that his measurements are real. Let's first prove that what we are looking at is NOT a simulation in software but real *analog* measurements of the output as I mentioned.
First his measurements:
Now let's compare it to the software simulation of the same by Ethan with a -9dbfs signal:
We immediately see lots of differences:
1. The noise floor is not flat and is some 40 db higher than Ethan's simulations. We know that real DACs cannot achieve 24 bits of dynamic range and that is the case with author's measurement.
2. You see those two little peaks after the original tone? They are at 200 Hz and 300 HZ with the original tone being at 100Hz. What are they? Harmonic distortions created by a *real* DAC. They do not exist in Ethan's simulations because he assumes an ideal DAC.
So we know that what he did was that he played a low level signal and then made a measurement on the *analog output of his system.* This is important because we very well could have had a gain stage in either the playback system or the measurement.
As Rock mentioned, the level of quantization distortion remains the same when you decimate a signal down to 16 bits but relative to a low level signal, its strength can sharply increase as a percentage of it. So I simulated what would happen if you took a ~-50db fs "low level" signal, in my case at 32 bit samples, and chopped it down to 16 bits (NOT 8). Then I amplified it so that the amplitude of the main 100 Hz signal was similar to the author's. This is what I got:
Let's compare it now to author's real life measurements:
While I did not try to match my simulations 100% to his, and his is a real device and mine is a simulation, you can see that in both cases even though our samples are 16 bits, our distortion relative to our signal has risen way higher. It is a simple matter of what happens when our source signal is low in level and you amplify it and the noise with it as you play.
The situation demonstrates what I always say about digital: it is a superb system for reproducing loud signals. If you want to see what a digital system doesn't do as well, you need to look at low level signals. In this scenario, if someone recorded music at -50db fs and you turned up the volume to listen to it, you would be hearing the distortion which in this case would serve to make the sound harsher as it adds all of those higher frequency harmonics -- kind of like what happens if your amplifier was clipping.
Remember again, I was not trying to demonstrate anything here but the fact that dither does what it says it does. That was author's goal and was also mine. That the dithered signal had none of these spikes.
If we can get you to own up to your own mistakes the discussion can proceed.
You not only think I am wrong, but a third-party that did the above tests and another person who quoted it. Earlier it was Bob Stuart that was also wrong, writing corporate white paper rather than something published by AES. So it is not just me that you think is wrong but others not in the conversation.
On the technical front, you imply that the DAC low pass filtering which exists *above* our hearing range gets rid of harmonics *in* our hearing range. This is an impossibility of course unless you are playing a semantic game of saying they are not pure square waves. Yous said that distortions in time domain do not map to the same in frequency domain, violating the most fundamental theories of signal processing (Fourier). It is important that we get the theory right here as that is *objective*.
Earlier in the thread, you had no trouble believing Monty's statement that ultrasonic tones create audible results in the audible frequency band proven by some listening test. I questioned it since it had no backing. I explained how a full amplitude 26 Khz signal was not a realistic situation. So in both cases, I was taking the position of inaudibility but you were the believer. I could have really ran with his statement there. But it was not right to do that based on what he was saying.